What does the solution of $$(3x-8)(x+5)

The solution represents the values of $$x$$ for which the product of the two factors is negative, indicating the intervals where the quadratic expression is below the x-axis.

How do you determine the intervals for the solution of $$\frac{(x-4)(4x-5)}{0}$$ ?

Find the roots of the equation $$(x-4)(4x-5)=0$$ , which are $$x=4$$ and $$x=\frac{5}{4}$$ . Test intervals around these roots to find where the product is greater than or equal to zero.

What does the inequality $$y

It represents the region below the parabola defined by $$y=(x+4)^2+1$$ .

What is the role of the discriminant in quadratic inequalities?

The discriminant, given by $$D=b^2-4ac$$ , determines the nature of the roots of the quadratic equation. If $$D>0$$ , there are two distinct real roots; if $$D=0$$ , there is one real root; and if $$D

What does it mean if a quadratic inequality has no solution?

It means that the quadratic expression does not satisfy the inequality for any real value of $$x$$ , often occurring when the parabola is entirely above or below the x-axis.

How can you check your solution to a quadratic inequality?

Substitute values from the solution intervals back into the original inequality to verify if they satisfy the condition.

What is the importance of testing intervals in solving quadratic inequalities?

Testing intervals helps determine where the quadratic expression is positive or negative, which is essential for finding the solution set.

A parabola is the graph of a quadratic function, characterized by its U-shape, which can open upwards or downwards depending on the sign of the leading coefficient.

What does the term 'critical points' refer to in quadratic inequalities?

Critical points are the x-values where the quadratic expression equals zero or where the inequality changes from true to false, typically the roots of the equation.

How do you graph a quadratic inequality?

Graph the corresponding quadratic equation as a solid or dashed line (depending on the inequality) and shade the appropriate region based on the inequality sign.

Quadratic Inequalities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic inequality?

Back

2.

FLASHCARD QUESTION

Front

How do you solve a quadratic inequality?

Back

To solve a quadratic inequality, first find the roots of the corresponding quadratic equation. Then, test intervals between the roots to determine where the inequality holds true.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It represents the maximum or minimum value of the function.

5.

FLASHCARD QUESTION

Front

Back

The graph is a parabola that opens upwards, shifted left by 3 units and down by 3 units. The region above the parabola represents the solution to the inequality.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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